A uniqueness theorem for reverse biased diodes

Abstract

We analyze the basic semiconductor device equations in the case of a symmetric one-dimensional reverse biased diode. The “classical” proofs of uniqueness theorems for this nonlinear system are based on asynlptotic methods and are not valid for arbitrary values of the applied bias. The main result of this paper is that every symmetric solution of this system is locally unique for any reverse bias value. Our method is based oq a “decoupling” of the associated linearized system and on the generalized maximum principle.

Keywords:

• Nonlinear System
• elliptic
• Maximum principle
• semiconducter
• unique